WASHINGTON - A needle stored with a beer can appeared to contain an extremely tiny amount of Roger Clemens’s DNA, which turned out to be good news and bad news for both sides in the perjury trial of the seven-time Cy Young Award winner.

A forensic scientist on Friday linked Clemens to cotton balls and a syringe needle saved from an alleged steroids injection 11 years ago. His testimony, laced with statistics and probabilities, was one of the last pieces of the government’s case in its effort to prove that the pitcher lied to Congress in 2008 when he denied using performance-enhancing substances.

Under cross-examination, Clemens’s lawyer tried to poke holes in the physical evidence. He got the expert to acknowledge there were “hundreds of thousands’’ of white males in the United States who could be a match for the scant amount of DNA found on the needle, and that it’s “conceivable’’ the cotton balls could have been contaminated by beer and saliva.

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Prosecutors had hoped to wrap up their case heading into the long holiday weekend as the trial reached the end of its sixth week, but the DNA expert’s testimony took much longer than expected. US District Judge Reggie Walton then ended the session a half-hour early when one of the jurors learned that her mother had died.

The judge said he doesn’t expect the juror, a woman who works in law enforcement with the local public transportation authority, to return. Two jurors have previously been dismissed for sleeping, and another departure would leave only one alternate in a trial expected to last at least two more weeks.

The government’s key witness, longtime Clemens strength coach Brian McNamee, says he injected Clemens with steroids in 1998, 2000 and 2001, and with human growth hormone in 2000. He said he kept the needle and other waste from a 2001 injection and stored it in and around a beer can in a FedEx box in his home for more than six years before turning it over to federal investigators.

Alan Keel of Forensic Science Associates told jurors that the DNA found on two cotton balls was “unique to one person who has ever lived on the planet’’ - Clemens. He said that one of the cotton balls had a random match possibility of one in 15.4 trillion for Clemens’s DNA, and the other was one in 173 trillion, when compared with the population of white people in the US.

But the needle was not as conclusive. Keel was able to detect only six to 12 cells for testing when he examined it. A drop of blood, by comparison, contains up to 30,000 cells.

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The match: one in 449 for Clemens.

“That means that Mr. Clemens is the likely source of that biology,’’ Keel said.

Knowing that the defense would attempt to undermine the integrity of the evidence, prosecutor Courtney Saleski asked: “Is there any way to fake this?’’

“No,’’ said Keel, shaking his head. “If this were contrived, I would expect to obtain much more biological material.’’

During cross-examination, Clemens lawyer Michael Attanasio attacked the findings in several ways. He pointed out that Keel was being paid by the government. He pointed out that Keel didn’t test all of the items available. He pointed out that the DNA had degraded over time. He noted that 449 was a “far, far smaller number’’ than the other numbers in the trillions, and it therefore can’t be said with uncontested certainty that the DNA on the needle belongs to Clemens.